1.1 Description of Fluid Motion 1 --
1.2 Choice of Coordinate System 2 --
1.3 Pathlines, Streak Lines, and Streamlines 3 --
1.4 Forces in a Fluid 4 --
1.5 Integral Form of the Fluid Dynamic Equations 6 --
1.6 Differential Form of the Fluid Dynamic Equations 8 --
1.7 Dimensional Analysis of the Fluid Dynamic Equations 14 --
1.8 Flow with High Reynolds Number 17 --
1.9 Similarity of Flows 19 --
2 Fundamentals of Inviscid, Incompressible Flow 21 --
2.1 Angular Velocity, Vorticity, and Circulation 21 --
2.2 Rate of Change of Vorticity 24 --
2.3 Rate of Change of Circulation: Kelvin's Theorem 25 --
2.4 Irrotational Flow and the Velocity Potential 26 --
2.5 Boundary and Infinity Conditions 27 --
2.6 Bernoulli's Equation for the Pressure 28 --
2.7 Simply and Multiply Connected Regions 29 --
2.8 Uniqueness of the Solution 30 --
2.9 Vortex Quantities 32 --
2.10 Two-Dimensional Vortex 34 --
2.11 Biot-Savart Law 36 --
2.12 Velocity Induced by a Straight Vortex Segment 38 --
2.13 Stream Function 41 --
3 General Solution of the Incompressible, Potential Flow Equations 44 --
3.1 Statement of the Potential Flow Problem 44 --
3.2 General Solution, Based on Green's Identity 44 --
3.3 Summary: Methodology of Solution 48 --
3.4 Basic Solution: Point Source 49 --
3.5 Basic Solution: Point Doublet 51 --
3.6 Basic Solution: Polynomials 54 --
3.7 Two-Dimensional Version of the Basic Solutions 56 --
3.8 Basic Solution: Vortex 58 --
3.9 Principle of Superposition 60 --
3.10 Superposition of Sources and Free Stream: Rankine's Oval 60 --
3.11 Superposition of Doublet and Free Stream: Flow around a Cylinder 62 --
3.12 Superposition of a Three-Dimensional Doublet and Free Stream: Flow around a Sphere 67 --
3.13 Some Remarks about the Flow over the Cylinder and the Sphere 69 --
3.14 Surface Distribution of the Basic Solutions 70 --
4 Small-Disturbance Flow over Three-Dimensional Wings: Formulation of the Problem 75 --
4.1 Definition of the Problem 75 --
4.2 Boundary Condition on the Wing 76 --
4.3 Separation of the Thickness and the Lifting Problems 78 --
4.4 Symmetric Wing with Nonzero Thickness at Zero Angle of Attack 79 --
4.5 Zero-Thickness Cambered Wing at Angle of Attack-Lifting Surfaces 82 --
4.6 Aerodynamic Loads 85 --
4.8 Linearized Theory of Small-Disturbance Compressible Flow 90 --
5 Small-Disturbance Flow over Two-Dimensional Airfoils 94 --
5.1 Symmetric Airfoil with Nonzero Thickness at Zero Angle of Attack 94 --
5.2 Zero-Thickness Airfoil at Angle of Attack 100 --
5.3 Classical Solution of the Lifting Problem 104 --
5.4 Aerodynamic Forces and Moments on a Thin Airfoil 106 --
5.5 Lumped-Vortex Element 114 --
5.6 Summary and Conclusions from Thin Airfoil Theory 120 --
6 Exact Solutions with Complex Variables 122 --
6.1 Summary of Complex Variable Theory 122 --
6.2 Complex Potential 125 --
6.3 Simple Examples 126 --
6.4 Blasius Formula, Kutta-Joukowski Theorem 128 --
6.5 Conformal Mapping and the Joukowski Transformation 128 --
6.6 Airfoil with Finite Trailing-Edge Angle 137 --
6.7 Summary of Pressure Distributions for Exact Airfoil Solutions 138 --
6.8 Method of Images 141 --
6.9 Generalized Kutta-Joukowski Theorem 146 --
7 Perturbation Methods 151 --
7.1 Thin-Airfoil Problem 151 --
7.2 Second-Order Solution 154 --
7.3 Leading-Edge Solution 157 --
7.4 Matched Asymptotic Expansions 160 --
7.5 Thin Airfoil between Wind Tunnel Walls 163 --
8 Three-Dimensional Small-Disturbance Solutions 167 --
8.1 Finite Wing: The Lifting Line Model 167 --
8.2 Slender Wing Theory 184 --
8.3 Slender Body Theory 195 --
8.4 Far Field Calculation of Induced Drag 201 --
9 Numerical (Panel) Methods 206 --
9.1 Basic Formulation 206 --
9.2 Boundary Conditions 207 --
9.3 Physical Considerations 209 --
9.4 Reduction of the Problem to a Set of Linear Algebraic Equations 213 --
9.5 Aerodynamic Loads 216 --
9.6 Preliminary Considerations, Prior to Establishing Numerical Solutions 217 --
9.7 Steps toward Constructing a Numerical Solution 220 --
9.8 Example: Solution of Thin Airfoil with the Lumped-Vortex Element 222 --
9.9 Accounting for Effects of Compressibility and Viscosity 226 --
10 Singularity Elements and Influence Coefficients 230 --
10.1 Two-Dimensional Point Singularity Elements 230 --
10.2 Two-Dimensional Constant-Strength Singularity Elements 232 --
10.3 Two-Dimensional Linear-Strength Singularity Elements 237 --
10.4 Three-Dimensional Constant-Strength Singularity Elements 244 --
10.5 Three-Dimensional Higher Order Elements 258 --
11 Two-Dimensional Numerical Solutions 262 --
11.1 Point Singularity Solutions 262 --
11.2 Constant-Strength Singularity Solutions (Using the Neumann B.C.) 276 --
11.3 Constant-Potential (Dirichlet Boundary Condition) Methods 288 --
11.4 Linearly Varying Singularity Strength Methods (Using the Neumann B.C.) 298 --
11.5 Linearly Varying Singularity Strength Methods (Using the Dirichlet B.C.) 306 --
11.6 Methods Based on Quadratic Doublet Distribution (Using the Dirichlet B.C.) 315 --
11.7 Some Conclusions about Panel Methods 323 --
12 Three-Dimensional Numerical Solutions 331 --
12.1 Lifting-Line Solution by Horseshoe Elements 331 --
12.2 Modeling of Symmetry and Reflections from Solid Boundaries 338 --
12.3 Lifting-Surface Solution by Vortex Ring Elements 340 --
12.4 Introduction to Panel Codes: A Brief History 351 --
12.5 First-Order Potential-Based Panel Methods 353 --
12.6 Higher Order Panel Methods 358 --
12.7 Sample Solutions with Panel Codes 360 --
13 Unsteady Incompressible Potential Flow 369 --
13.1 Formulation of the Problem and Choice of Coordinates 369 --
13.2 Method of Solution 373 --
13.3 Additional Physical Considerations 375 --
13.4 Computation of Pressures 376 --
13.5 Examples for the Unsteady Boundary Condition 377 --
13.6 Summary of Solution Methodology 380 --
13.7 Sudden Acceleration of a Flat Plate 381 --
13.8 Unsteady Motion of a Two-Dimensional Thin Airfoil 387 --
13.9 Unsteady Motion of a Slender Wing 400 --
13.10 Algorithm for Unsteady Airfoil Using the Lumped-Vortex Element 407 --
13.11 Some Remarks about the Unsteady Kutta Condition 416 --
13.12 Unsteady Lifting-Surface Solution by Vortex Ring Elements 419 --
13.13 Unsteady Panel Methods 433 --
14 Laminar Boundary Layer 448 --
14.1 Concept of the Boundary Layer 448 --
14.2 Boundary Layer on a Curved Surface 452 --
14.3 Similar Solutions to the Boundary Layer Equations 457 --
14.4 Von Karman Integral Momentum Equation 463 --
14.5 Solutions Using the von Karman Integral Equation 467 --
14.6 Weak Interactions, the Goldstein Singularity, and Wakes 471 --
14.7 Two-Equation Integral Boundary Layer Method 473 --
14.8 Viscous-Inviscid Interaction Method 475 --
14.9 Concluding Example: The Flow over a Symmetric Airfoil 479 --
15 Enhancement of the Potential Flow Model 483 --
15.2 Coupling between Potential Flow and Boundary Layer Solvers 487 --
15.3 Influence of Viscous Flow Effects on Airfoil Design 495 --
15.4 Flow over Wings at High Angles of Attack 505 --
15.5 Possible Additional Features of Panel Codes 528 --
A Airfoil Integrals 537 --
B Singularity Distribution Integrals 540 --
C Principal Value of the Lifting Surface Integral I[subscript L] 545 --
D Sample Computer Programs 546.
